Retinal Blood Vessels Modeling based on Fuzzy Sobel Edge Detection

and Morphological Segmentation

Jan Kubicek

, Juraj Timkovic

, Marek Penhaker

, David Oczka

, Alice Krestanova

Martin Augustynek

and Martin Cerny

VSB–Technical University of Ostrava, FEECS, K450, 17 listopadu 15, 708 33, Ostrava–Poruba, Czech Republic

Clinic of Ophthalmology, University Hospital Ostrava, Czech Republic

Keywords: Retinal Blood Vessels, RetCam 3, Sobel Operator, Fuzzy, Image Edge.

Abstract: In the clinical ophthalmology, the retinal blood vessels processing represent a significant issue regarding the

clinical diagnosis. A level of the blood vessels curvature may serve as a reliable indicator of the

pathological process. For curvature estimation, a precise model of the retinal blood vessels is necessary. In

this paper, we propose a method based on the sensitive edge detector utilizing the fuzzy rules and

morphological techniques. The fuzzy edge detector is able to even detect edges while suppressing the high

frequency image noise in the non-contrast environment where the image spatial characteristics are weak.

Consequent morphological operations serve for adjustment of the segmentation procedure to obtain the

smooth model which effectively separates the retinal blood vessels from the retinal background. In the final

step, we obtain the binary mathematical model of the retinal blood vessels. We have verified the proposed

method against the gold standard images. We have applied the proposed solution on the low-contrast retinal

data from the RetCam 3 which is standard for Retinopathy of prematurity. Mostly, when using the RetCam

3, the retinal data has lower contrast therefore, the segmentation procedure is supposed to be robust, even in

the noisy environment.

1 RETINAL IMAGE

PROCESSING

Retinal image processing is one of the crucial tasks

for the ophthalmologic practice. In the retinal area

we can recognize several structures being clinically

evaluated. The optical disc (optical nerve) is

clinically perceived as a central point of the retinal

structure. It is also a starting point where the

beginning of the retinal blood vessels is observable.

Optical disc is utilized as a reference point when the

retinal lesions are present to track their dynamical

progress over the time because the optical disc

geometrical features should be stable over the time.

Regarding a lot of clinical reasons, the retinal

blood vessels are perceived as the most important

clinical structure for the retinal diagnosis. On the

base of the blood vessels curvature (clinically called

tortuosity) we can at least estimate whether the

retina exhibits signs of the pathological process.

Generally it supposed that no retinal blood vessel is

narrow, but it is curved in the whole length.

Nevertheless, we recognize an extreme curving

which can be observed as oscillating waves is some

parts of the blood vessels (Fig. 1).

Judging by a current state of the

ophthalmological practice, the software tools

allowing for automatic modeling and quantification

of the retinal blood vessels would significantly

contribute to the precise diagnosis. Currently, there

is a lack of such software instruments which would

generate the retinal mathematical models. It may be

caused by several reasons. There are more clinical

imaging alternatives for the retinal visualization,

especially fundus cameras and retinal probes. These

devices give images in different resolution, and

other spatial features. Regarding segmentation

procedure effectivity, it is supposed the worse image

features images have, the worse segmentation

accuracy we achieve. We primarily process the data

from the retinal probes (RetCam 3) which have a

worse image features, therefore the segmentation

procedure should have higher sensitivity against the

image noise, and simultaneously should be robust

even in the low-contrast environment. When

Kubicek, J., Timkovic, J., Penhaker, M., Oczka, D., Krestanova, A., Augustynek, M. and Cerny, M.

Retinal Blood Vessels Modeling based on Fuzzy Sobel Edge Detection and Morphological Segmentation.

DOI: 10.5220/0007237501210126

In Proceedings of the 12th International Joint Conference on Biomedical Engineering Systems and Technologies (BIOSTEC 2019), pages 121-126

ISBN: 978-989-758-353-7

121

comparing with the Fundus camera data processing,

for the RetCam 3 data the segmentation procedure is

supposed to be robust even in the noisy

environment. (Tan 2016; Meng 2015; Wankhede

2015)

Figure 1: Comparison of a retina with the physiological

blood vessels (left) – vessels are direct, and blood vessels

having the pathological tortuosity signs in a form of the

oscillations (right).

2 RELATED WORK

Generally, there are many segmentation techniques

available in the recent literature. It is important to

mention that mostly of them are intended to the

fundus images processing having a great resolution

and other spatial characteristics. We are focused on

different type of data (RetCam 3) having

significantly different image features even though

imaging same retinal area. Therefore, research in

this area is important.

Mostly, the segmentation techniques involve

stages as the image preprocessing which is focused

to improving the contrast between the blood vessels

and retinal image background, and own

segmentation procedure which detects the blood

vessels system. The techniques can be categorized

on: (a) Kernel-based techniques (Omasundaram

2017) , (b) retinal vessel tracking (Omasundaram

2017; Mapavi 2015), (c) multiscale techniques (Ben

2018; Wang 2017; Kaur 2016; Huang 2017), (d)

model-based (Annunziata 2016; Lazar 2015), (e)

adaptive local thresholding (Palomera-Pérez 2010;

Yan 2018; Zou 2018) and (f) machine learning

(Khan 2018; Mapavi 2015).

Performance of each segmentation approach is

evaluated by many metrics. The most common

parameters are: True positive rate (TPR), average

false positive rate (FPR), average sensitivity (TPR),

average specificity (FPR), average accuracy and

precision. From the view of the clinical practice,

sensitivity and specificity represent the most

frequently metrics in the medical research. The

higher specificity and sensitivity we achieve, the

better results we obtain. (Hatanaka 2018)

The recent literature does not contain a lot of

information about the processing the low-contrast

retinal images. Since the most of the presented

algorithms have been primarily tested on the fundus

images having a great resolution we have no

information about robustness and sensitivity of the

segmentation methods for the low-contrast images.

Our paper just brings a significant contribution in

this area. (Omasundaram 2017), (Melo, 2018)

3 DESIGN OF SEGMENTATION

METHOD

In this section, we introduce a segmentation

algorithm for modeling of the retinal blood vessels.

In our approach, we want to avoid using the image

preprocessing as one of the conventional steps of

many approaches. The image preprocessing intended

for an improvement of the spatial image

characteristic with the goal of contrast boosting

between blood vessels and adjacent retinal

structures. Unfortunately, each preprocessing

algorithm at least partially modifies the pixel’s

intensity characteristics. Thus, the original clinical

information is modified. In our approach, we

consciously exclude these procedures. The proposed

algorithm is composed from two essential parts

including the edge detection and morphological

segmentation procedure.

3.1 Sobel Operator Driven by Fuzzy

Logic Rules

The Sobel operator belongs to a group of the

gradient edge detectors. This method computes

partial derivation of the image signal in the

horizontal (



) and vertical direction (



Image gradient representing the edges in both

directions is given:



















(1)

Generally, the main disadvantage of the gradient

edge operator is an inclination to the image noise

having significantly different intensity spectrum than

the image background. This phenomenon is given by

the hard thresholding of the horizontal and vertical

gradient. Such hard thresholding is not capable

classifying the image edge and noise.

We have optimized the Sobel operator by using

the fuzzy rules. In the fuzzy model, each gradient

direction is characterized by the Gaussian

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membership function (Fig. 2). The final

classification of the edge pixels is driven by the

triangular membership function (Fig. 3).

Figure 2: Gaussians membership functions for horizontal

gradient (



) and vertical gradient (



Figure 3: Triangular membership functions representing

the edge classification.

On the Fig. 4, we report the fuzzy edge detection

on the non-contrast retinal image. Important aspect

of the detector is an elimination of the optical disc,

and simultaneous boosting of the retinal blood

vessels.

Figure 4: Native retinal image from the RetCam 3 with

resolution 640x480 px (left) and result of the Sobel

detector driven by the fuzzy rules (right).

3.2 Morphological Image Segmentation

Morphological operations are commonly intended

for adjustment of the binary images. In our

approach, we are using a sequence of the

morphological operations for adjustment of the

spatial characteristic of the retinal blood vessels.

Firstly, we apply the morphological dilatation.

Dilatation sums of two sets with using of the

Minkowski sum. By applying this procedure, we

achieve the object expansion in the binary image,

and mainly filling the holes. Such procedure

compensates a sensitivity of the edge detection when

non-homogenous intensity distribution. The

dilatation is defined by the following way:

⨁ ∈



,,∈,∈

(2)

Where X stands for the binary image and B is the

structural element, characterizing a shape of the

dilatation. Here, we are using the square matrix 3x3.

In the next step, we are using the morphological

closing as the dilatation with erosion with the same

structural element. By this procedure, we achieve

smoothing curves better representing the real blood

vessels connecting of tiny holes and also removing

of small holes. Closing is similar in some ways to

dilation in that it tends to enlarge the boundaries of

foreground (bright) regions in an image (and shrink

background color holes in such regions), but it is

less destructive of the original boundary shape. The

morphological operation closing is defined by the

following expression:

∘ ⨁⊝

(3)

In the last part of the segmentation model, the

binary skeleton is applied. We need to represent the

blood vessels by one pixel line thickness in order to

mathematically describe curvature of the individual

blood vessel’s pixels. Output is a typological

skeleton precisely describing shape of retinal blood

vessel system. This process is given by the following

definition:

⨁⨂

(4)

This iteration process is terminated when two

gradual steps achieve same results.

⨁









⨁



⨁



…⨁





(5)

Individual steps of the morphological operations are

depicted on the Fig. 5.

Figure 5: Process of the morphological operations:

dilatation, morphological opening and erosion.

Retinal Blood Vessels Modeling based on Fuzzy Sobel Edge Detection and Morphological Segmentation

123

4 TESTING AND QUANTITATIVE

COMPARISON

We cooperate with the Ophthalmological clinic of

the University hospital of Ostrava on the task of the

retinal blood vessels processing. We were given a

dataset containing 120 patients. These images have

been used for the testing of the segmentation

algorithm. This database is structuralized into

physiological and pathological blood vessels. All the

data have been acquired by the retinal probe RetCam

3 having the image resolution 640x480 px.

The input data are stored in the RGB format

being represented by three dimensional matrixes.

Each such matrix represents one channel of the RGB

model. We have experimentally found out that G

channel reliably reflects area of the blood vessels

while other channels nearly do not bring information

about the retinal blood vessels. Therefore, we have

done the RGB model decomposition with

consequent extraction of the G (green) channel (Fig.

6).

Figure 6: Extraction of green channel (left) and its

monochromatic conversion (right).

For the testing, we have divided the retinal

records into two groups, depending on their spatial

characteristics: contrast and non-contrast data. Since

it cannot be ensured that data will be always

acquired in a good contrast, we are primarily

focused on the non-contrast data to demonstrate

segmentation function in a worse environment (Fig.

7). The segmentation results are provided in the

binary mathematical model classifying the blood

vessels (white) from the image background (black).

Figure 7: Testing extract of the segmentation procedure

for four non-contrast native images.

In the last part of the model building, retinal

blood vessel have been skeletonized and fused.

Image fusion is an important procedure performing

the overlaying of the binary model with the native

records (Fig. 8).

Figure 8: Native retinal data (left column), binary skeleton

(middle column) and image fusion (right column).

In the last part of the analysis, we have performed a

quantitative comparison to objectification of the

segmentation process. We have analyzed the

segmentation performance against the ground truth

data representing the gold standard. This gold

standard has been done by the manual segmentation

performed by the clinical ophthalmologic expert. In

order to proper testing of the segmentation

robustness, we have done a comparison against

native image data and same records corrupted by the

salt and pepper noise and Gaussian noise.

The segmentation performance has been

evaluated based on the four metrics. Rand index (RI)

measures a level of the similarity between the binary

model against the gold standard. Structural similarity

(SSIM) measures a mutual structure. 2D correlation

(2D corr) measures a level of the linear dependence.

These parameters are normalized in a range [0; 1]

where 0 indicates no similarity, contrarily 1 stands

for completely identical results. A last parameter is

the Mean Squared Error (MSE) which measures an

average quadratic difference between the

segmentation result and the gold standard. Average

values of the parameters are reported in the Table 1.

Table 1: Quantitative comparison of the segmentation

model against the gold standard.

Native

data

Gaussian

noise

(0.1, 0.05)

Gaussian

noise

(0.1, 0.1)

Salt and

Pepper

(0.05)

Salt and

Pepper

(0.1)

Salt and

Pepper

(0.3)

0.91 0.84 0.77 0.83 0.78 0.71

SSIM

0.84 0.65 0.55 0.89 0.66 0.61

D cor

0.98 0.91 0.88 0.87 0.74 0.65

MSE

33.12 36.22 41.21 35.88 51.12 55.67

Based on the quantitative comparison it is apparent

that artificial noise slightly influences the

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segmentations results. The worst results are reported

when adding the Salt and Pepper noise. This noise is

strongly manifested as the binary signal which

significantly visually impairs the native retinal data.

5 CONCLUSIONS

The retinal image analysis has a significant impact

to practice of the clinical ophthalmology. In

comparison with the subjective analysis performed

by the clinical experts, the automatic segmentation

and modeling has unexceptionable benefits. Mainly,

it’s a relevant reproducibility of the clinical results

and features extraction allowing for classification of

the pathological blood vessels.

In our work, we have proposed the segmentation

model based on a combined approach of the Sobel

edge detector driven by the fuzzy rules and the

morphological operations. Conventional gradient

edge detectors lack of robustness in the noisy

environment, and insufficient contrast. It is also case

of the processing the retinal records from the retinal

probes which typically have lower resolution and

worse spatial features. Soft gradient thresholding of

the edge detector ensures robustness against image

noise. Judging by the experimental results, the fuzzy

edge detector is capable of efficiently detect contour

of the low-contrast blood vessels contours.

The morphological operations serve for

optimization of the edge detector with a target of

suppressing image noise and inhomogeneity. Final

model of the blood vessels is given by the blood

vessels skeleton and image fusion. We have

analyzed the blood vessels modeling against the gold

standard images. We have analyzed native image

records and noisy images (Gaussian and Salt and

Pepper noise). Judging by the results, the

segmentation model is able to reliably work even in

the noisy environment. It is a good prediction for

using in the clinical conditions where we cannot

ensure stable conditions of measurement.

ACKNOWLEDGMENTS

The work and the contributions were supported by

the project SV4508811/2101Biomedical

Engineering Systems XIV’. This study was also

supported by the research project The Czech Science

Foundation (GACR) 2017 No. 17-03037S

Investment evaluation of medical device

development run at the Faculty of Informatics and

Management, University of Hradec Kralove, Czech

Republic. This study was supported by the research

project The Czech Science Foundation (TACR)

ETA No. TL01000302 Medical Devices

development as an effective investment for public

and private entities.

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